QUOTIENTS OF CONIC BUNDLES

Abstract

Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over Open image in new window by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any quotient is birationally equivalent to a quotient of other k-rational conic bundle cyclic group \( {\mathrm{\mathfrak{C}}}_{2^k} \) of order 2k, dihedral group \( {\mathfrak{D}}_{2^k} \) of order 2k, alternating group \( {\mathfrak{A}}_4 \) of degree 4, symmetric group \( {\mathfrak{S}}_4 \) of degree 4 or alternating group \( {\mathfrak{A}}_5 \) of degree 5 effectively acting on the base of the conic bundle. Also we construct infinitely many examples of such quotients which are not k-birationally equivalent to each other.